Method of making group III nitride-based compound semiconductor

ABSTRACT

A method of making a group III nitride-based compound semiconductor has the steps of: providing a semiconductor substrate with a polished surface, the semiconductor substrate being of group III nitride-based compound semiconductor; and growing a semiconductor epitaxial growth layer of group III nitride-based compound semiconductor on the semiconductor substrate. The polished surface is an inclined surface that has an off-angle θ of 0.15 degrees or more and 0.6 degrees or less to a-face, c-face or m-face of the semiconductor substrate.

The present application is based on Japanese patent application No.2003-284859, the entire contents of which are incorporated herein byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a method of making a group III nitride-basedcompound semiconductor. This method is useful for the fabrication ofvarious semiconductor devices, such as a semiconductor light emittingelement and a semiconductor light receiving element.

2. Description of the Related Art

Conventionally, a technique is known that so called off angle(off-orientation) is introduced to the crystal growth surface of acrystal growth substrate so as to grow a high-quality semiconductorcrystal. See, for example, Japanese patent application laid-open Nos.2000-174395 (prior art 1), 2000-156348 (prior art 2), 2001-160539 (priorart 3) 2002-16000 (prior art 4) and 2003-60318 (prior art 5), andTsunenobu KIMOTO and Hiroyuki MATSUNAMI, “Step-controlled epitaxy insemiconductor SiC polytypes”, OYO BUTURI, vol. 64, No. 7, pp. 691-694(1995) (prior art 6).

The typical or general function and principle of the step-flow growthinduced by the setting of off-angle is described in prior art 6.

Prior arts 1 and 2 describe about trying to grow a high-quality groupIII nitride-based compound semiconductor on a heterosubstrate, such assapphire, ZnO and spinel, of a different kind from the targeted growthlayer (group III nitride-based compound semiconductor).

Prior arts 3 to 5 state that an off angle of 1 degree or more isdesirable.

In growing a group III nitride-based compound semiconductor on aheterosubstrate, the matching of lattice constant on crystal growthsurface is critical. Therefore, it is necessary to grow a buffer layerthereon to obtain a high-quality growth layer (semiconductor crystal).Thus, the method of using the heterosubstrate is not always desirable interms of the quality and the number of fabrication steps concerning thetargeted group III nitride-based compound semiconductor.

FIG. 1 is a schematic perspective view illustrating the problems ofconventional techniques. As shown in FIG. 5, if the off angle is set tobe more than 1 degree, the problem of step amplification occurs. Forexample, when a c-face of crystal growth substrate 1 of group IIInitride-based compound semiconductor (e.g., GaN) is polished whilehaving the off angle, a step portion y of about 1 atom layer to severaltens of atom layers is formed on the polished surface σ. Subsequently,when a growth layer 2 of group III nitride-based compound semiconductor(e.g., GaN) is grown on the polished surface a with the step portion y,a giant step Y that the height of step portion y is amplified may begenerated on the upper side of growth layer 2. In this case, the widthof a terrace (the interval of parallel giant steps Y) can be alsosignificantly greater than that of the atom-layer height-formed stepportion y on the polished surface σ.

The height of giant step Y is likely to increase according as the offangle of crystal growth substrate 1 increases. If the height of giantstep Y becomes too high, the flatness of growth layer 2 (targeted groupIII nitride-based compound semiconductor) obtained thereupon willdeteriorate. When using it for high-quality semiconductor devices,unignorable problems in terms of driving efficiency (current, voltage),operation life, heat generation etc.

On the other hand, if the off angle of crystal growth substrate 1 is toosmall, the growth layer 2 cannot grow based on the step-flow growth and,therefore, it is impossible to obtain a semiconductor crystal that has agood crystalline quality and a sufficiently flat surface. This can beproved by the general function and principle of step-flow growth asdescribed in prior art 6.

SUMMARY OF THE INVENTION

It is an object of the invention to provide a method of making a groupIII nitride-based compound semiconductor that can offer a goodcrystalline quality and a sufficiently flat surface to the resultingsemiconductor epitaxial growth layer.

It is another object of the invention to provide a method of making agroup III nitride-based compound semiconductor that can offer increasedefficiency.

Meanwhile, the above objects may be attained separately by any one ofsolutions of the invention, and it is not always guaranteed that onesolution can solve simultaneously all of the problems.

The next solutions are effective in solving the above problems.

(1) According to the first solution of the invention, a method of makinga group III nitride-based compound semiconductor comprises the steps of:

-   -   providing a semiconductor substrate with a polished surface, the        semiconductor substrate being of group III nitride-based        compound semiconductor; and    -   growing a semiconductor epitaxial growth layer of group III        nitride-based compound semiconductor on the semiconductor        substrate,    -   wherein the polished surface is an inclined surface that has an        off-angle θ of 0.15 degrees or more and 0.6 degrees or less to        a-face, c-face or m-face of the semiconductor substrate.

FIG. 2 is a perspective view illustrating a general definition ofoff-angle θ in case of c-face growth.

For example, when the off-angle θ as defined above is introduced bypolishing the c-face while removing a portion g, the normal vector ofpolished surface σ on the crystal growth substrate 1 of group IIInitride-based compound semiconductor is directed to a direction beinginclined by the same off-angle from a c-axis, as shown in FIG. 2, wherethe off-angle θ is emphasized for illustration purpose.

The next equation (A) is established when the off-angle θ issufficiently small:θ²=θ₁ ²+θ₂ ²  (A)where θ1 is an off-angle to an a-axis direction (a rotation angle aroundan m-axis to the c-face of polished surface σ), and θ2 is an off-angleto the m-axis direction (a rotation angle around the a-axis to thec-face of polished surface σ) Although in FIG. 2 the case of c-facegrowth is illustrated, the same definition can be also used in the caseof a-face growth and m-face growth.

Herein, “group III nitride-based compound semiconductor” includescompound semiconductors that are of two-element, three-element orfour-element, have an arbitrary mixed crystal ratio, and are representedby a general formula: Al_(1-x-y)Ga_(y)In_(x)N (0≦x≦1, 0≦y≦1, and0≦1−x−y≦1). Further, the group III nitride-based compound semiconductorincludes the compound semiconductors with p-type and/or n-type impuritydoped thereinto.

At least part of the group III element mentioned above may be replacedby boron (B), thallium (Tl) etc. At least part of nitrogen (N) maybereplaced by phosphorous (P), arsenic (As), antimony (Sb), bismuth (Bi)etc.

The p-type impurity (acceptor) mentioned above may include a knownp-type impurity such as magnesium (Mg) and calcium (Ca).

The n-type impurity (donor) mentioned above may include a known n-typeimpurity such as silicon (Si), sulfur (S), selenium (Se), tellurium (Te)and germanium (Ge).

The p-type or n-type impurity (acceptor or donor) of two or moreelements may be simultaneously contained. The p-type and n-typeimpurities may be simultaneously contained.

In growing the growth layer 2 (group III nitride-based compoundsemiconductor) on the semiconductor substrate, various growth methodssuch as MOVPE, HVPE, MBE and MOHVPE (metalorganic hydrogen chloridevapor phase epitaxy) described in prior art 7 as listed below may beused. Prior art 7: “preparation of Large Freestanding GaN Substrates byHydride Vapor Phase Epitaxy Using GaAs as a Starting Substrate”,JAPANESE JOURNAL OF APPLIED PHYSICS, Vol. 40 (2001) pp.L140-L143, Part2, No. 2B, 15 Feb. 2001.

By the first solution of the invention, the growth layer (group IIInitride-based compound semiconductor) can be grown on the semiconductorsubstrate (group III nitride-based compound semiconductor) while havingthe off-angle necessary and sufficient for inducing the step-flowgrowth. If the off-angle is too small, the step-flow growth cannot beinduced sufficiently. On the other hand, if the off-angle is too big,the problem of giant step (Y in FIG. 1) described earlier will occur.Thus, it is desired that the off-angle is set in the above-mentionedrange so as to obtain a growth layer with a high crystalline quality anda sufficiently flat surface.

By the first solution, the growth layer (group III nitride-basedcompound semiconductor) with a high crystalline quality and asufficiently flat surface can be obtained. When the growth layer isapplied to a semiconductor device, the semiconductor device will besignificantly advantageous in terms of driving efficiency (current,voltage), operation life, heat generation etc. For example, when thegrowth layer is used as a substrate for semiconductor laser, thesemiconductor laser can enjoy low threshold current, low consumedcurrent, high output and long operation life.

Further, by the first solution, a high crystalline quality growth layer(group III nitride-based compound semiconductor) can be obtained withoutusing the buffer layer. Therefore, the number of fabrication steps canbe advantageously reduced.

Although some crystal growth apparatuses cannot be used for aluminum(Al), the above solution can be applied to even such apparatuses.

(2) According to the second solution of the invention, in the firstsolution, the polished surface is a c-face in its principle surface, andthe off-angle θ is 0.2 degrees or more and 0.35 degrees or less.

When the second solution (0.2 degrees≦θ≦0.35 degrees) is applied to thecase of using the c-face as principle surface polished, it is known byexperience that the growth layer can have a further high crystallinequality.

(3) According to the third solution of the invention, in the first orsecond solution, the method further comprises the step of:

-   -   providing a stripe-shaped specific region on the polished        surface, the specific region being composed of a material that        prevents the growth of the group III nitride-based compound        semiconductor on its surface,    -   wherein the specific region is provided on the polished surface        such that the longitudinal direction of the specific region        intersects with the longitudinal direction of a step portion        that is formed with an atom-layer height on the polished surface        by introducing the off-angle θ.

The stripe-shaped specific region may be formed such that the stripe islocally disconnected in the longitudinal direction.

By the third solution of the invention, since the stripe-shaped specificregion that is not likely to be a crystal growth surface intersectswith, i.e., being not parallel to, the step portion, a situation (growthstate) that the stripe-shaped specific region completely interferes withthe step-flow growth using the step portion as the starting point(nucleus) can be avoided.

Thus, by the third solution, since the specific region is not likely tointerfere with step-flow growth, the probability that the growth mode ofstep-flow growth is shifted to the growth mode of two-dimensionalnucleus generation can lower. As a result, the growth mode of step-flowgrowth can be well maintained. Thus, the crystal growth surface with ahigh crystalline quality and a sufficiently flat surface can beobtained.

(4) According to the fourth solution of the invention, in the thirdsolution, the stripe-shaped specific region is of an amorphous maskmaterial.

For example, the mask material may be a material used in theconventional ELO method. The specific region may be of an arbitrarymaterial if the material can prevent the growth of the group IIInitride-based compound semiconductor on the surface. For example, astripe-shaped ELO mask is available that is used in conducting so-calledfacet-controlled ELO as described prior arts 8 and 9 listed below. Priorart 8: “Transmission Electron Microscopy Investigation of Dislocationsin GaN Layer Grown by Facet-controlled Epitaxial Lateral Overgrowth”,JAPANESE JOURNAL OF APPLIED PHYSICS, Vol. 40 (2001) pp.L309-L312, Part2, No. 4A, 1 Apr. 2001. Prior art 9: Mizutani et al., “Reduction ofDislocations in GaN by FACELO (Facet-controlled ELO)”, TECHNICAL REPORTOF IEICE, ED2000-22, CPM2000-7, SDM2000-22(2000-05), pp. 35-40.

By the fourth solution of the invention, the specific region can beeasily composed of (designed and formed by using) an amorphous maskmaterial by using known general methods such as a masking technique forELO mask.

(5) According to the fifth solution of the invention, in the first orsecond solution, the method further comprises the step of:

-   -   providing a stripe-shaped specific region on the polished        surface, the specific region being composed of a structure that        has a relatively low growth speed in growing the group III        nitride-based compound semiconductor on its surface,    -   wherein the specific region is provided on the polished surface        such that the longitudinal direction of the specific region        intersects with the longitudinal direction of a step portion        that is formed with an atom-layer height on the polished surface        by introducing the off-angle θ.

The stripe-shaped specific region may be formed such that the stripe islocally disconnected in the longitudinal direction.

The stripe-shaped specific region may be a region that is composed ofpolycrystal locally formed on the semiconductor substrate or a regionthat is composed of a crystal surface different from the other principleregion (i.e., a region other than the specific region). The specificregion may be composed of an arbitrary structure if the structure has arelatively low growth speed in growing the group III nitride-basedcompound semiconductor on the surface.

Especially, the next solution is provided to cope with a stripe-shapedregion called “core regions” as described in prior art 10 listed below.Prior art 10: “Extremely Long Lifetime Blue-violet Laser Diodes GrownHomoepitaxially on GaN Substrates”, Extended Abstracts of the 2002International Conference on Solid State Devices and Materials, Nagoya,2002, pp. 832-833.

By the fifth solution of the invention, since the stripe-shaped specificregion that has a relatively low crystal growth speed intersects with,i.e., being not parallel to, the step portion, a situation (growthstate) that the stripe-shaped specific region completely interferes withthe step-flow growth using the step portion as the starting point(nucleus) can be avoided.

Thus, by the fifth solution, since the specific region is not likely tointerfere with step-flow growth, the probability that the growth mode ofstep-flow growth is shifted to the growth mode of two-dimensionalnucleus generation can lower. As a result, the crystal growth surfacewith a high crystalline quality and a sufficiently flat surface can beobtained.

The specific region may be intentionally formed on the substrateprovided, or may be formed by the method of removing a defect such asdislocation from main part of a targeted device.

(6) According to the sixth solution of the invention, in the fifthsolution, the stripe-shaped specific region is composed of a crystaldefect-concentrated region that crystal defects of group IIInitride-based compound semiconductor are locally and denselyconcentrated.

Such a crystal defect-concentrated region is described in prior art 10.A substrate with a stripe-shaped region called “core regions” is knownand is in common use. The crystal defect-concentrated region may beformed by properly combining crystal growth methods as described inprior arts 7 listed earlier, 11 and 12 listed below. Prior art 11:Japanese patent application laid-open No. 2001-102307. Prior art 12:“Growth and Characterization of Freestanding GaN Substrates”, Journal ofCrystal Growth 237-239 (2002) 912-921.

By the sixth solution of the invention, the crystal defect-concentratedregion as described in prior art 7, which is previously formed on thesubstrate, can be used as the specific region.

(7) According to the seventh solution of the invention, in any one ofthe third to sixth solutions, a plurality of the stripe-shaped specificregions are formed nearly in parallel with each other on the polishedsurface.

By the sixth solution of the invention, even when the plurality ofstripe-shaped specific regions are formed, the probability that thegrowth mode of step-flow growth is shifted to the growth mode oftwo-dimensional nucleus generation can lower. As a result, the crystalgrowth surface with a high crystalline quality and a sufficiently flatsurface can be obtained.

(8) According to the eighth solution of the invention, in any one of thethird to seventh solutions, the longitudinal direction of thestripe-shaped specific region is nearly orthogonal to the longitudinaldirection of a step portion that is formed with an atom-layer height onthe polished surface by introducing the off-angle θ.

If the stripe-shaped specific region intersects with the longitudinaldirection of step portion, the step-flow growth can be theoreticallycontinued regardless of the measure of intersection angle. However, asdefined by the eighth solution, it is desirable that the stripe-shapedspecific region is nearly orthogonal to the longitudinal direction ofstep portion. In this case, since the growth direction of step-flowgrowth nearly coincides with the longitudinal direction of step portion,the stripe-shaped specific region does not interfere with the step-flowgrowth using the step portion as the starting point (nucleus) during thecrystal growth. Thus, by the eighth solution, the growth mode ofstep-flow growth can be stably and continuously maintained. As a result,the crystal growth surface with a high crystalline quality and asufficiently flat surface can be obtained.

(9) According to the ninth solution of the invention, in any one of thethird to eighth solutions, the longitudinal direction of thestripe-shaped specific region is set to be parallel to an m-axisdirection of the semiconductor substrate.

By the ninth solution of the invention, a resonator of semiconductorlaser can be placed in parallel with the stripe direction (longitudinaldirection) of specific region.

A resonator of edge emission type semiconductor laser uses generally anm-face that is easy to obtain a mirror surface by cleavage. Thus, by thearrangement of the ninth solution, the resonator can be disposed suchthat it is not located over the stripe-shaped specific region.Therefore, the resonator disposed is not negatively affected by thespecific region and is provided with an edge of good quality.Accordingly, the ninth solution can offer a high crystalline quality anda good edge flatness to the resonator.

Thus, by the ninth solution, a good growth layer can be obtained that isversatile enough to be used as a resonator of edge emission typesemiconductor laser.

BRIEF DESCRIPTION OF THE DRAWINGS

The preferred embodiments according to the invention will be explainedbelow referring to the drawings, wherein:

FIG. 1 is a schematic perspective view illustrating the problems ofconventional techniques;

FIG. 2 is a perspective view illustrating a general definition ofoff-angle θ in case of c-face growth;

FIG. 3A is a photomicrograph showing a crystal growth surface of growthlayer after crystal growth when setting the off-angle θ to be 0.11degrees;

FIG. 3B is a photomicrograph showing a crystal growth surface of growthlayer after crystal growth when setting the off-angle θ to be 0.24degrees;

FIG. 4 is a schematic perspective view showing a growth layer 2 grown inthe case that the polished surface a of semiconductor substrate 1 has astripe-shaped specific region that is composed of a crystaldefect-concentrated region; and

FIGS. 5A to 5C are photomicrographs showing a c-face of growth layer 2in the case of forming a stripe-shaped specific region S.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[First Embodiment]

FIGS. 3A and 3B are photomicrographs showing a crystal growth surface ofthe growth layer 2 after crystal growth when setting the off-angle θ tobe 0.11 degrees (01=0.04 degrees, θ2=0.10 degrees) and 0.24 degrees(θ1=0.24 degrees, θ2=0.02 degrees), respectively in the structure asshown in FIG. 2. The semiconductor substrate 1 (FIG. 2) used therein isprepared by growing a high-quality semiconductor crystal of galliumnitride (GaN) by HVPE. In polishing the portion g, a slurry of about 1μm is used on the final polishing stage.

The growth layers 2 as shown in FIGS. 3A and 3B are made under the samecrystal growth conditions. The process of growing the growth layer 2will be explained below.

At first, the semiconductor substrate 1 (θ=0.11 degrees, 0.24 degrees)after the polishing is washed and then is preliminarily heated to 1150°C.

Then, while keeping the semiconductor substrate 1 at 1150° C., thegrowth layer 2 of GaN with a thickness of 6 μm is grown on the polishedsurface a by MOVPE. The materials used thereat are trimethylgallium(Ga(CH₃)₃) and ammonium (NH₃). Flow gas H₂ is supplied at 10litters/min., NH₃ at 10 litters/min., and TMG (Ga(CH₃)₃) at 2.0×10⁻⁴mol/.

As shown in FIG. 3B, the crystal growth surface of growth layer 2 isflattened. It can be thus estimated that the step-flow growth issmoothly conducted by setting the off-angle to be 0.24 degrees. Incontrast, as shown in FIG. 3A, the crystal growth surface of growthlayer 2 is not flattened. It can be thus estimated that the growth modeof step-flow growth is not established due to setting the off-angle tobe so small, 0.11 degrees.

[Second Embodiment]

FIG. 4 is a schematic perspective view showing a growth layer 2 grown inthe case that the polished surface σ of semiconductor substrate 1 has astripe-shaped specific region that is composed of a crystaldefect-concentrated region. On the polished surface σ, there areprovided a flat region with reduced crystal defect and with high crystalquality, and the crystal defect-concentrated region that are repeatedwith a certain period A (≈0.400 μm) in the a-axis direction. Thestripe-shaped specific region S is compose of the crystaldefect-concentrated region, and has a stripe width of about 50 μm. Thus,an interval L between neighboring stripes is about 350 μM.

The semiconductor substrate 1 used in the second preferred embodiment isa GaN substrate produced by Sumitomo Electric Industries, Ltd.

The crystal defect-concentrated region is described in prior art 10. Asubstrate with a stripe-shaped region called “core regions” is known andis in common use. The crystal defect-concentrated region may be formedby properly combining crystal growth methods as described in prior arts7, 11 and 12.

The targeted growth layer 2 of gallium nitride (GaN) is not likely togrow on the stripe-shaped specific region S. Therefore, the source gasesremaining without being used for the crystal growth over the specificregion S are additionally supplied to the both edges of stripe-shapedspecific region S. Thereby, at the edge portion, the upward growth speedis locally increased and, as a result, a pulse portion f is formed alongthe edge of growth layer 2.

In FIG. 4, y′ indicates a step portion generated on the crystal growthsurface of growth layer 2.

FIGS. 5A to 5C are photomicrographs showing a c-face of growth layer 2in the case of forming a stripe-shaped specific region S. These samplesare grown using the structure as shown in FIG. 4 and the same crystalgrowth process (MOVPE) as in the first embodiment described earlier. Theoff-angle is differentiated among the samples as shown in FIGS. 5A to5C.

The setting of off-angle, as defined in FIG. 2, for the samples in FIGS.5A to 5C is as follows:

<Example of This Embodiment: FIG. 5A>θ1=0.01 degrees, θ2=0.24 degrees  (B)<Comparative Example: FIG. 5B>θ1=0.23 degrees, θ2=0.01 degrees  (C)<Comparative Example: FIG. 5C>θ1=0.04 degrees, θ2=0.03 degrees  (D)

With regard to the off-angle, only the example of this embodiment inFIG. 5A satisfies the next formula (E):

<Desired Setting of Off-Angle>θ²≈θ₂ ² (θ₁<<θ₂<1 deg), 0.2 deg≦θ≦0.35  (E)

The conditions of crystal growth shown in the example of embodiment 2(FIG. 5A) meet the limitations defined in claims 1 to 7 attached herein.As a result, the growth layer 2 can be obtained that has a good flatnessand a crystalline quality. Because of this, it is estimated that thefunctions and effects of the invention defined in claims 1 to 7 are allembodied in the example of embodiment 2 (FIG. 5A).

[Advantages of the Invention]

The growth layer (group III nitride-based compound semiconductor)obtained according to the invention can offer an excellent semiconductorcrystal material. Hence, the growth layer of the invention is veryuseful for various semiconductor devices, such as a semiconductor lightemitting element such as a light emitting diode and a semiconductorlaser, a semiconductor light receiving element, and semiconductorpressure sensor. Especially, it can widely serve as a crystal growingsubstrate of an electric device.

Although the invention has been described with respect to the specificembodiments for complete and clear disclosure, the appended claims arenot to be thus limited but are to be construed as embodying allmodifications and alternative constructions that may occur to oneskilled in the art which fairly fall within the basic teaching hereinset forth.

1. A method of making a group III nitride-based compound semiconductor,comprising the steps of: providing a semiconductor substrate with apolished surface, the semiconductor substrate being of group IIInitride-based compound semiconductor; and growing a semiconductorepitaxial growth layer of group III nitride-based compound semiconductoron the semiconductor substrate, wherein the polished surface is aninclined surface that has an off-angle θ of 0.15 degrees or more and 0.6degrees or less to a-face, c-face or m-face of the semiconductorsubstrate.
 2. The method according to claim 1, wherein: the polishedsurface is a c-face in its principle surface, and the off-angle θ is 0.2degrees or more and 0.35 degrees or less.
 3. The method according toclaim 1 further comprising the step of: providing a stripe-shapedspecific region on the polished surface, the specific region beingcomposed of a material that prevents the growth of the group IIInitride-based compound semiconductor on its surface, wherein thespecific region is provided on the polished surface such that thelongitudinal direction of the specific region intersects with thelongitudinal direction of a step portion that is formed with anatom-layer height on the polished surface by introducing the off-angleθ.
 4. The method according to claim 3, wherein: the stripe-shapedspecific region is of an amorphous mask material.
 5. The methodaccording to claim 1 further comprising the step of: providing astripe-shaped specific region on the polished surface, the specificregion being composed of a structure that has a relatively low growthspeed in growing the group III nitride-based compound semiconductor onits surface, wherein the specific region is provided on the polishedsurface such that the longitudinal direction of the specific regionintersects with the longitudinal direction of a step portion that isformed with an atom-layer height on the polished surface by introducingthe off-angle θ.
 6. The method according to claim 5, wherein: thestripe-shaped specific region is composed of a crystaldefect-concentrated region that crystal defects of group IIInitride-based compound semiconductor are locally and denselyconcentrated.
 7. The method according to claim 3, wherein: a pluralityof the stripe-shaped specific regions are formed nearly in parallel witheach other on the polished surface.
 8. The method according to claim 3,wherein: the longitudinal direction of the stripe-shaped specific regionis nearly orthogonal to the longitudinal direction of a step portionthat is formed with an atom-layer height on the polished surface byintroducing the off-angle θ.
 9. The method according to claim 3,wherein: the longitudinal direction of the stripe-shaped specific regionis set to be parallel to an m-axis direction of the semiconductorsubstrate.